[Phys-L] Fermi question on state borders
Being in the spirit of a Fermi question, I don't think we are **allowed**
to look stuff up. We are supposed to reason our way though.
By "Continental" USA I assume we mean the contiguous 48. Which is close
enough to 50 and we don't need to worry about Alaska. I would consider the
contiguous 48 to be a rectangle. Without looking anything up, I'm guessing
we are about 4,000 km wide by 2,000 km tall.
4k X 2k = 8 M km^2
8 M km^2 divided by 50 states (48 rounded up) is 1.6 times million divided
by ten.
That's 1.6 times 100,000 km^2 or about 2 times ten to the 5 (2E5)
km-squared per state.
The box states are probably rectangles but close enough to a square. The
length of each side of a square is the square root of the area. Thus, each
average box state is square root of 2E5.
In my head, it is easier to do square roots of even powers so take the
square root of 20E4.
Square root of twenty is about four and a half (4 squared is 16, 5 squared
is 25, so guess at 4.5 for the root of 20.) Likewise, the square root of
1E4 is 1E2 = 100.
I now have the average size of one side of a state is 4.5 * 100 or 450 km.
We have made so many approximations that fussing over integrals and the
like is a waste of time. I'm going to assume that, on average, you will be
halfway from one side to the center.
So, half of 450 km = 225 km.
*So my final answer is 200 km with a precision of one significant figure.*
How close am I?
John
- - - -
John E. Sohl, Ph.D.
WSU Brady Presidential Distinguished Professor Emeritus
Department of Physics and Astronomy
Department of Environmental Science
Department of Being Retired and Loving It
Weber State University
cell: (801) 476-0589 (Text me, I don't answer the phone if you are not in
my contacts.)